Proton spin-lattice relaxation dispersion of liquid crystal polymers: Characterization of local and collective motions

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Abstract
This paper reports on studies of the longitudinal proton spin relaxation dispersion T1Z(ω) of a nematic main chain liquid crystal polymer (M̄n=30 000) over a very broad Larmor frequency range (1 kHz≤ω/2π≤120 MHz). Analysis of the experiments is achieved in terms of a density operator treatment employing the Redfield approximation. The results show that collective motions contribute to the proton spin relaxation process in the kilohertz regime, as found for low molar mass liquid crystals, whereas the conventional megahertz range is dominated by reorientation of individual molecules. The intramolecular motions consist of trans–gauche isomerization and phenyl ring flips. These motions are the fastest in the hierarchy of time with correlation times of 10−10 s in the nematic melt of the polymer at T≊460 K. The intermolecular (whole molecule) motions are interpreted as rotational diffusion in an orienting potential. They exhibit a T1Z(ω)∼ω0.65 dispersion in the megahertz range and have correlation times ranging from 10−9 to 10−7 s at this temperature. The slowest motions affecting longitudinal spin relaxation can be assigned to nematic order director fluctuations characterized by a broad distribution of thermally activated modes. Analysis of the dispersion profiles in the kilohertz regime provides the viscoelastic parameters of the main chain liquid crystal polymer. At T=460 K, an average elastic constant of K=8×10−11 N and an effective viscosity of η=1×103 Pa s have been determined. Using the experimentally accessible value for the short wavelength cutoff of the elastic modes, one obtains the mean‐square amplitude of the director fluctuations <θ02≳=0.02, corresponding to a director order parameter of SOF=0.98. Thus, the contributions of the collective chain motions to the measured order parameters are negligible.